Re: Index Laws Practice

Hi kmlb123!Happy to learn that you found this Exercise useful!I shall post more exercises at Middle School/High School level;certainly I shall try to post an exercise exclusively on Coordinate Geometry.

Re: Index Laws Practice

Hi Toast! Nice set of problems!

Here is a variation of law 2 that is easy to use and always ends up with a non-negative exponent.It takes care of all three cases: m>n, m=n, m<n. It is especially nice when the problem involvesnegative exponents.

(p is the opposite of the smaller of m and n) For example recalling that a^0 = 1 we get( Whether this is true for a=0 has been thoroughly explored in other threads of this forum.)

Of course the last two cases here would obviously be 1 from the start.

This law takes care of all cases for positive, negative or zero exponents m and n, leaving the answer with a non-negative exponent for a in the numerator or denominator as most booksrequire for the answer.

If p is anything else but -min(m,n) the equality is still true, but it will not be in "simplified" form.

Play around with it a bit and I think you will find it is quite handy and easy to use.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).LaTex is like painting on many strips of paper and then stacking them to see what picture they make.